Well, concerning omniscience, any set cannot contain a subset that is larger than the set itself, therefore the universe cannot contain an omnisicent mind, that is, a mind that knows all. I guess it's possible in a fantasy sort of way that a framework could be set up so that the mind doesn't know all, but can observe what it needs to observe at any time - instead of storing the information in itself - that could be viewed as *functionally* omniscient (but that's cheating, and you'd have to be in a universe in which pesky things like the uncertainy principle don't apply). If there is a 'higher order' of reality above this one, there could be a mind that is omniscient about our universe (being a subset) but not omniscient about its own.

As for the universe being aware... Well, we're part of the universe, aren't we? It isn't as we exist outside of it and just observe it. You'll have to better frame the question, I think, because I'm not sure what you're asking.

You are obviously thinking of universes being aware in a human type way. Which would be naive. But you could instead think about the way the "laws of nature" are said to apply everywhere, at all times. Nothing escapes their attention. That is a kind of omni-quality. A kind of "mind" as some philosophers have argued.